Simplify The Expression: $\[ 3 \sqrt{a} + 8 \sqrt{a} - 9 \sqrt{a} \\]
Understanding the Problem
In this problem, we are given an algebraic expression involving square roots. The expression is: 3√a + 8√a - 9√a. Our goal is to simplify this expression by combining like terms and eliminating any unnecessary components.
What are Like Terms?
Like terms are terms that have the same variable raised to the same power. In this case, all three terms have the variable 'a' raised to the power of 1/2 (since it's a square root). Therefore, we can combine these terms by adding or subtracting their coefficients.
Simplifying the Expression
To simplify the expression, we need to combine the like terms. We can do this by adding or subtracting the coefficients of the like terms.
3√a + 8√a - 9√a
First, let's combine the coefficients of the like terms:
(3 + 8)√a - 9√a
Next, let's simplify the expression by combining the coefficients:
11√a - 9√a
Now, let's combine the like terms by adding or subtracting their coefficients:
(11 - 9)√a
Finally, let's simplify the expression by evaluating the expression inside the parentheses:
2√a
Conclusion
In this problem, we simplified the expression 3√a + 8√a - 9√a by combining like terms and eliminating any unnecessary components. We started by identifying the like terms and then combined their coefficients. Finally, we simplified the expression by evaluating the expression inside the parentheses.
Key Takeaways
- Like terms are terms that have the same variable raised to the same power.
- To simplify an expression, we need to combine like terms by adding or subtracting their coefficients.
- We can simplify an expression by evaluating the expression inside the parentheses.
Real-World Applications
Simplifying expressions is an important skill in mathematics and has many real-world applications. For example, in physics, we often need to simplify complex expressions to solve problems. In engineering, we need to simplify expressions to design and build complex systems.
Common Mistakes
When simplifying expressions, it's easy to make mistakes. Here are some common mistakes to avoid:
- Not identifying like terms
- Not combining like terms correctly
- Not simplifying the expression by evaluating the expression inside the parentheses
Practice Problems
Here are some practice problems to help you practice simplifying expressions:
- Simplify the expression: 2√x + 5√x - 3√x
- Simplify the expression: 4√y - 2√y + 3√y
- Simplify the expression: 6√z + 2√z - 4√z
Answer Key
- (2 + 5 - 3)√x = 4√x
- (4 - 2 + 3)√y = 5√y
- (6 + 2 - 4)√z = 4√z
Simplify the Expression: 3√a + 8√a - 9√a - Q&A =====================================================
Q: What are like terms in an algebraic expression?
A: Like terms are terms that have the same variable raised to the same power. In the expression 3√a + 8√a - 9√a, all three terms have the variable 'a' raised to the power of 1/2 (since it's a square root). Therefore, we can combine these terms by adding or subtracting their coefficients.
Q: How do I simplify an expression with like terms?
A: To simplify an expression with like terms, you need to combine the like terms by adding or subtracting their coefficients. In the expression 3√a + 8√a - 9√a, we can combine the coefficients of the like terms as follows:
(3 + 8)√a - 9√a
Next, we simplify the expression by combining the coefficients:
11√a - 9√a
Finally, we combine the like terms by adding or subtracting their coefficients:
(11 - 9)√a
Q: What is the final simplified expression?
A: The final simplified expression is 2√a.
Q: What are some common mistakes to avoid when simplifying expressions?
A: Some common mistakes to avoid when simplifying expressions include:
- Not identifying like terms
- Not combining like terms correctly
- Not simplifying the expression by evaluating the expression inside the parentheses
Q: How do I identify like terms in an expression?
A: To identify like terms in an expression, you need to look for terms that have the same variable raised to the same power. In the expression 3√a + 8√a - 9√a, all three terms have the variable 'a' raised to the power of 1/2 (since it's a square root). Therefore, we can combine these terms by adding or subtracting their coefficients.
Q: Can you provide some practice problems to help me practice simplifying expressions?
A: Here are some practice problems to help you practice simplifying expressions:
- Simplify the expression: 2√x + 5√x - 3√x
- Simplify the expression: 4√y - 2√y + 3√y
- Simplify the expression: 6√z + 2√z - 4√z
Q: What are some real-world applications of simplifying expressions?
A: Simplifying expressions is an important skill in mathematics and has many real-world applications. For example, in physics, we often need to simplify complex expressions to solve problems. In engineering, we need to simplify expressions to design and build complex systems.
Q: How do I know if I have simplified an expression correctly?
A: To know if you have simplified an expression correctly, you need to check your work by:
- Making sure you have identified all the like terms
- Combining the like terms correctly
- Simplifying the expression by evaluating the expression inside the parentheses
Q: Can you provide some tips for simplifying expressions?
A: Here are some tips for simplifying expressions:
- Make sure you have identified all the like terms
- Combine the like terms correctly
- Simplify the expression by evaluating the expression inside the parentheses
- Check your work by plugging in values for the variables
Q: What are some common expressions that can be simplified?
A: Some common expressions that can be simplified include:
- Expressions with like terms, such as 3√a + 8√a - 9√a
- Expressions with variables raised to the same power, such as 2x^2 + 5x^2 - 3x^2
- Expressions with fractions, such as 1/2 + 1/4 - 1/8
Q: Can you provide some examples of expressions that cannot be simplified?
A: Here are some examples of expressions that cannot be simplified:
- Expressions with unlike terms, such as 3√a + 8x^2 - 9y
- Expressions with variables raised to different powers, such as 2x^2 + 5x - 3y^2
- Expressions with fractions that cannot be combined, such as 1/2 + 1/3 - 1/4